Effect of microscopic disorder on magnetic properties of metamaterials

We analyze the effect of microscopic disorder on the macroscopic properties of composite metamaterials and study how weak statistically independent fluctuations of the parameters of the structure elements can modify their collective magnetic response and left-handed properties. We demonstrate that even a weak microscopic disorder may lead to a substantial modification of the metamaterial magnetic properties, and a 10% deviation in the parameters of the microscopic resonant elements may lead to a substantial suppression of the wave propagation in a wide frequency range. A noticeable suppression occurs also if more than 10% of the resonant magnetic elements possess strongly different properties, and in the latter case the defects can create an additional weak resonant line. These results are of a key importance for characterizing and optimizing novel composite metamaterials with the left-handed properties at terahertz and optical frequencies

Wave Function Shredding by Sparse Quantum Barriers

We discuss a model in which a quantum particle passes through $\delta$ potentials arranged in an increasingly sparse way. For infinitely many barriers we derive conditions, expressed in terms ergodic properties of wave function phases, which ensure that the point and absolutely continuous parts are absent leaving a purely singularly continuous spectrum. For a finite number of barriers, the transmission coefficient shows extreme sensitivity to the particle momentum with fluctuation in many different scales. We discuss a potential application of this behavior for erasing the information carried by the wave function.Comment: 4 pages ReVTeX with 3 epsf figure

Anderson localization in metamaterials and other complex media

We review some recent (mostly ours) results on the Anderson localization of light and electron waves in complex disordered systems, including: (i) left-handed metamaterials, (ii) magneto-active optical structures, (iii) graphene superlattices, and (iv) nonlinear dielectric media. First, we demonstrate that left-handed metamaterials can significantly suppress localization of light and lead to an anomalously enhanced transmission. This suppression is essential at the long-wavelength limit in the case of normal incidence, at specific angles of oblique incidence (Brewster anomaly), and in the vicinity of the zero-epsilon or zero-mu frequencies for dispersive metamaterials. Remarkably, in disordered samples comprised of alternating normal and left-handed metamaterials, the reciprocal Lyapunov exponent and reciprocal transmittance increment can differ from each other. Second, we study magneto-active multilayered structures, which exhibit nonreciprocal localization of light depending on the direction of propagation and on the polarization. At resonant frequencies or realizations, such nonreciprocity results in effectively unidirectional transport of light. Third, we discuss the analogy between the wave propagation through multilayered samples with metamaterials and the charge transport in graphene, which enables a simple physical explanation of unusual conductive properties of disordered graphene superlatices. We predict disorder-induced resonances of the transmission coefficient at oblique incidence of the Dirac quasiparticles. Finally, we demonstrate that an interplay of nonlinearity and disorder in dielectric media can lead to bistability of individual localized states excited inside the medium at resonant frequencies. This results in nonreciprocity of the wave transmission and unidirectional transport of light.Comment: 37 pages, 30 figures, Review pape

Soliton transmission through a disordered system

An exact formula for the transmission time in a disordered nonlinear soliton-bearing classical one-dimensional system is obtained

Quasiperiodic Envelope Solitons

We analyse nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics, the quasiperiodic soliton, which describes spatially localized self-trapping of a quasiperiodic wave. We point out a link between the quasiperiodic soliton and partially incoherent spatial solitary waves recently generated experimentally.Comment: Submitted to PRL. 4 pages with 5 figure

Infrared Spectroscopy of Quantum Crossbars

Infrared (IR) spectroscopy can be used as an important and effective tool for probing periodic networks of quantum wires or nanotubes (quantum crossbars, QCB) at finite frequencies far from the Luttinger liquid fixed point. Plasmon excitations in QCB may be involved in resonance diffraction of incident electromagnetic waves and in optical absorption in the IR part of the spectrum. Direct absorption of external electric field in QCB strongly depends on the direction of the wave vector ${\bf q}.$ This results in two types of $1D\to 2D$ dimensional crossover with varying angle of an incident wave or its frequency. In the case of QCB interacting with semiconductor substrate, capacitive contact between them does not destroy the Luttinger liquid character of the long wave QCB excitations. However, the dielectric losses on a substrate surface are significantly changed due to appearance of additional Landau damping. The latter is initiated by diffraction processes on QCB superlattice and manifests itself as strong but narrow absorption peaks lying below the damping region of an isolated substrate.SubmiComment: Submitted to Phys. Rev.

Anderson Localization of Classical Waves in Weakly Scattering Metamaterials

We study the propagation and localization of classical waves in one-dimensional disordered structures composed of alternating layers of left- and right-handed materials (mixed stacks) and compare them to the structures composed of different layers of the same material (homogeneous stacks). For weakly scattering layers, we have developed an effective analytical approach and have calculated the transmission length within a wide region of the input parameters. When both refractive index and layer thickness of a mixed stack are random, the transmission length in the long-wave range of the localized regime exhibits a quadratic power wavelength dependence with the coefficients different for mixed and homogeneous stacks. Moreover, the transmission length of a mixed stack differs from reciprocal of the Lyapunov exponent of the corresponding infinite stack. In both the ballistic regime of a mixed stack and in the near long-wave region of a homogeneous stack, the transmission length of a realization is a strongly fluctuating quantity. In the far long-wave part of the ballistic region, the homogeneous stack becomes effectively uniform and the transmission length fluctuations are weaker. The crossover region from the localization to the ballistic regime is relatively narrow for both mixed and homogeneous stacks. In mixed stacks with only refractive-index disorder, Anderson localization at long wavelengths is substantially suppressed, with the localization length growing with the wavelength much faster than for homogeneous stacks. The crossover region becomes essentially wider and transmission resonances appear only in much longer stacks. All theoretical predictions are in an excellent agreement with the results of numerical simulations.Comment: 19 pages, 16 figures, submitted to PR

Controlling soliton refraction in optical lattices

We show in the framework of the 1D nonlinear Schrödinger equation that the value of the refraction angle of a fundamental soliton beam passing through an optical lattice can be controlled by adjusting either the shape of an individual waveguide or the relative positions of the waveguides. In the case of the shallow refractive index modulation, we develop a general approach for the calculation of the refraction angle change. The shape of a single waveguide crucially affects the refraction direction due to the appearance of a structural form factor in the expression for the density of emitted waves. For a lattice of scatterers, wave-soliton interference inside the lattice leads to the appearance of an additional geometric form factor. As a result, the soliton refraction is more pronounced for the disordered lattices than for the periodic ones

Nonreciprocal Anderson Localization in Magneto-Optical Random Structures

We study, both analytically and numerically, disorder-induced localization of light in random layered structures with magnetooptical materials. The Anderson localization in such structures demonstrates nonreciprocal features in the averaged localization length and individual transmission resonances. We employ short-wavelength approximation where the localization effects are strong, and consider both the Faraday and Voigt magnetooptical geometries. In the Faraday geometry, the transmission is strongly nonreciprocal for the circularly polarized waves, whereas in the Voigt geometry, the nonreciprocity is much weaker, and it may appear only for the individual transmission resonances of the TM-polarized waves.Comment: 8 pages, 6 figure